This paper presents the development of several models of a deep convolutional auto-encoder in the Caffe deep learning framework and their experimental evaluation on the example of MNIST dataset. We have created five models of a convolutional auto-encoder which differ architecturally by the presence or absence of pooling and unpooling layers in the auto-encoder's encoder and decoder parts. Our results show that the developed models provide very good results in dimensionality reduction and unsupervised clustering tasks, and small classification errors when we used the learned internal code as an input of a supervised linear classifier and multi-layer perceptron. The best results were provided by a model where the encoder part contains convolutional and pooling layers, followed by an analogous decoder part with deconvolution and unpooling layers without the use of switch variables in the decoder part. The paper also discusses practical details of the creation of a deep convolutional auto-encoder in the very popular Caffe deep learning framework. We believe that our approach and results presented in this paper could help other researchers to build efficient deep neural network architectures in the future.